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In his speech to America’s schoolchildren last month, President Obama had a clear directive about video games: Put them away. It wasn’t the first time he had sounded this particular alarm, warning of the dangers of days spent at gaming consoles. But the latest science shows that there’s a lot more to video games than their dark reputations suggest.

“There’s still a tendency to think of video games as a big wad of time-wasting content,’’ said Cheryl Olson, co-director of the Center for Mental Health and Media at Massachusetts General Hospital. “You would never hear a parent say we don’t allow books in our home, but you’ll still hear parents say we don’t allow video games in our home.

“Games are a medium. They’re not inherently good or bad.’’

After years of focusing on the bad - and there are still legitimate concerns, for instance, about the psychological effects of certain violent games - scientists are increasingly examining the potential benefits of video games. Their studies are revealing that a wide variety of games can boost mental function, improving everything from vision to memory. Still unclear is whether these gains are long-lasting and can be applied to non-game tasks. But video games, it seems, might actually be good for the brain.

The very structure of video games makes them ideal tools for brain training.

“Video games are hard,’’ said Eric Klopfer, the director of MIT’s Education Arcade, which studies and develops educational video games. “People don’t like to play easy games, and games have figured out a way to encourage players to persist at solving challenging problems.’’

The games aren’t just hard - they’re adaptively hard. They tend to challenge people right at the edge of their abilities; as players get better and score more points, they move up to more demanding levels of play. This adaptive challenge is “stunningly powerful’’ for learning, said John Gabrieli, a neuroscientist at MIT.

Most games involve a huge number of mental tasks, and playing can boost any one of them. Fast-paced, action-packed video games have been shown, in separate studies, to boost visual acuity, spatial perception, and the ability to pick out objects in a scene. Complex, strategy-based games can improve other cognitive skills, including working memory and reasoning.

These findings fit with scientists’ increasing understanding of how malleable the human brain truly is. Researchers now know that learning and practicing a challenging task can actually change the brain.

Richard Haier,a pediatric neurologist and professor emeritus at the School of Medicine at the University of California at Irvine, has shown in a pair of studies that the classic game Tetris, in which players have to rotate and direct rapidly falling blocks, alters the brain. In a paper published last month, Haier and his colleagues showed that after three months of Tetris practice, teenage girls not only played the game better, their brains became more efficient.

A type of scan that illuminates brain activity showed that at the end of the three months, the girls’ brains were working less hard to complete the game’s challenges. What’s more, parts of the cortex, the outer layer of their brains responsible for high-level functions, actually got thicker. Several of these regions are associated with visual spatial abilities, planning, and integration of sensory data.

“Does this mean that Tetris is good for your brain?’’ Haier said. “That is the big question. We don’t know that just because you become better at playing Tetris after practice and your brain changes . . . whether those changes generalize to anything else.’’

Generalizability to non-game situations is the big question surrounding other emerging games, particularly software that is being marketed explicitly as a way to keep neurons spry as we age. The jury is still out on whether practicing with these games helps people outside of the context of the game. In one promising 2008 study, however, senior citizens who started playing Rise of Nations, a strategic video game devoted to acquiring territory and nation building, improved on a wide range of cognitive abilities, performing better on subsequent tests of memory, reasoning, and multitasking. The tests were administered after eight weeks of training on the game. No follow-up testing was done to assess whether the gains would last.

Now that researchers know these off-the-shelf games can have wide-ranging benefits, they’re trying to home in on the games’ most important aspects, potentially allowing designers to create new games that specifically boost brain power.

“Until now, people have been asking can you learn anything from games?’’ MIT’s Klopfer said. “That’s a less interesting question than what aspects of games are important for fostering learning.’’

Klopfer is currently conducting research to determine how important narrative is in an educational physics game: Do students learn more with a more narrative game? And Anne McLaughlin, a psychologist who co-directs the Gains Through Gaming lab at North Carolina State University, is assessing whether games that are novel, include social interaction, and require intense focus are better at boosting cognitive skills. McLaughlin and her colleagues will use the findings to design games geared toward improving mental function among the elderly.

Other researchers are hoping to use video games to encourage prosocial behaviors - actions designed to help others. (“Prosocial’’ behaviors are, in some ways, the opposite of “antisocial’’ ones.) In June, an international team of researchers, including several from Iowa State University, reported that middle school students in Japan who played games in which characters helped or showed affection for others, later engaged in more of these behaviors themselves. Researchers also found that US college students randomly assigned to play a prosocial game were subsequently kinder to a fellow research subject than students who played violent or neutral games.

Unlike, say, movies or books, video games don’t just have content, they also have rules. A game is set up to reward certain actions and to punish others. This means they have immense potential to teach children ethics and values, said Scott Seider, an assistant professor of education at Boston University. (Of course, this is a double-edged sword. Games could reward negative, antisocial behavior just as easily as positive, prosocial behavior.)

Some off-the-shelf games already contain strong prosocial themes; consider The Sims, for instance, or the classic Oregon Trail, which make players responsible for the well-being of other characters and feature characters who take care of one another. But Seider also hopes game developers consider the prosocial possibilities in developing new games. The challenge for the architects of future games will be figuring out how to wrap virtuous characteristics into an engaging package.

“Ultimately, the video game needs to be an entertaining experience,’’ Seider said. “The game has to be fun.’’